Finite Group Databasebeta

← #30604505

Subgroups — #30604505

Order 15616.

320 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462178C211yesmaximal, characteristic, complemented
2D61⋊(C4⋊C16)C211yesmaximal, characteristic, complemented
3#21460786C212yesmaximal, complemented
4D4⋊#11758187C212yesmaximal, complemented
5#21454797C211yesmaximal, characteristic
6C2×D61⋊C16—21no—
7#16840683—21no—
8#16840683—21no—
9C4⋊#11758187C2212yes—
10#16840657—21no—
11C4×#11758187C2212yes—
12#16840294C411yescharacteristic
13#16839892C411yescharacteristic
14#16839886C2211yescharacteristic
15#16839831—21no—
16D4×#92418C2211yescharacteristic
17#16839825—21no—
18#16839820—21no—
19#16839818C411yescharacteristic
20#16839720—21no—
21C4×C8×D61C2211yescharacteristic
22C61×#436C411yescharacteristic
23D61⋊C16—42no—
24C2×#11758187—22no—
25C2×#11758187—22no—
26C22×#92418—21no—
27C2×C8×D61D411yescharacteristic
28C2×C8×D61D411yescharacteristic
29#14519770—21no—
30#14519768C811yescharacteristic
31#14519764C811yescharacteristic
32#14519759—21no—
33#14519757C811yescharacteristic
34#14519748C811yescharacteristic
35C4×Dic122C2×C411yescharacteristic
36C4×C22⋊D61—21no—
37#14519736—21no—
38C42×D61C2×C411yescharacteristic
39C4⋊#92418C2×C411yescharacteristic
40#14519706—21no—
41#14519706—21no—
42C22⋊#92418—21no—
43#14519689—21no—
44#14519687—21no—
45#14519687—21no—
46C4×#92418C2311yescharacteristic
47C8×Dic61—21no—
48C8×Dic61D411yescharacteristic
49C8×Dic61D411yescharacteristic
50C2×M16×C61—21no—
51C4×D4×C61C2×C411yescharacteristic
52C4⋊C8×C61C2×C411yescharacteristic
53C22⋊C8×C61—21no—
54C4×C8×C61C2×C411yescharacteristic
55C2×D4×C61C2×C811yescharacteristic
56C22×C4×C61—21no—
57C2×C22⋊D61—21no—
58C2×C4×D61C22⋊C411yescharacteristic
59C2×C4×D61C2×C811yescharacteristic
60C2×C4×D61M1611yescharacteristic
61C2×Dic122C2×C811yescharacteristic
62M16×C61—42no—
63C2×C8×C61—21no—
64C2×C8×C61C22⋊C411yescharacteristic
65C2×C8×C61C22⋊C411yescharacteristic
66C4⋊C4×C61C2×C811yescharacteristic
67C22⋊C4×C61—21no—
68C42×C61C22×C411yescharacteristic
69C22⋊Dic61—21no—
70C22⋊Dic61—21no—
71C22⋊Dic61—21no—
72#11758198—21no—
73C4⋊Dic61—21no—
74C4⋊Dic61—21no—
75C4⋊Dic61C2×C811yescharacteristic
76#11758196—21no—
77#11758196—21no—
78C4×Dic61—21no—
79C4×Dic61C22⋊C411yescharacteristic
80C4×Dic61C2×C811yescharacteristic
81C4×Dic61M1611yescharacteristic
82C2×#92418—21no—
83C2×#92418—41no—
84C2×#92418—41no—
85C2×#92418C2×D411yescharacteristic
86C2×#92418C2×D411yescharacteristic
87C8×D61—21no—
88C8×D61—21no—
89C8×D61—41no—
90#11758187—42no—
91#11758187—42no—
92C23×C61—21no—
93C22×D61C22⋊C811yescharacteristic
94D4×C61—22no—
95C2×C4×C61—21no—
96C2×C4×C61—41no—
97C2×C4×C61—41no—
98C2×C4×C61C2×C22⋊C411yescharacteristic
99C2×C4×C61C22×C811yescharacteristic
100C2×C4×C61C2×M1611yescharacteristic
101C22⋊D61—42no—
102C2×Dic61—21no—
103C2×Dic61—21no—
104C2×Dic61C22⋊C811yescharacteristic
105C2×Dic61C22⋊C811yescharacteristic
106C2×Dic61C22⋊C811yescharacteristic
107C4×D61—22no—
108C4×D61—21no—
109C4×D61—21no—
110C4×D61—22no—
111Dic122—22no—
112C8×C61—21no—
113C8×C61—21no—
114C8×C61—41no—
115#92418—21no—
116#92418—41no—
117#92418AGL(1,ℤ/8)11yescharacteristic
118#92418#13711yescharacteristic
119#11622—611nomaximal, Sylow
120C22×C61—41no—
121C22×C61—41no—
122C22×C61—41no—
123C22×C61C2×C22⋊C811yescharacteristic
124C2×D61—21no—
125C2×D61—21no—
126C2×D61#35012yes—
127C4×C61—21no—
128C4×C61—41no—
129C4×C61#41711yescharacteristic
130C4×C61#42111yescharacteristic
131C4×C61#50412yes—
132Dic61—21no—
133Dic61—21no—
134Dic61—21no—
135Dic61—41no—
136Dic61—41no—
137#2966—611no—
138#2162—611no—
139C2×C4⋊C16—611no—
140Q8⋊C16—612no—
141D4⋊C16—612no—
142C2×C61—81no—
143C2×C61#147711yescharacteristic
144C2×C61#211311yescharacteristic
145C2×C61C2×#35011yescharacteristic
146D61—22no—
147#529—611no—
148C22×C16—1221no—
149#446—611no—
150C8×Q8—611no—
151#436#692311yescharacteristic
152#435—1221no—
153C8×D4—611no—
154C8×D4—1221no—
155#433—1221no—
156#432—611no—
157#405—1221no—
158C2×C4×C8—611no—
159C4⋊C16—612no—
160C4⋊C16—1221no—
161C4⋊C16—1221no—
162C22⋊C16—1221no—
163C4×C16—612no—
164C61#1162211yescharacteristic, complemented, Sylow
165C2×M16—21no—
166C22×C8—611no—
167C22×C8—611no—
168C22×C8—1221no—
169#126—1221no—
170#125—611no—
171#124—611no—
172#123—1221no—
173C22⋊Q8—611no—
174#121—611no—
175C4×Q8—611no—
176C4×D4—1221no—
177C4×D4C2×#692311yescharacteristic
178#117—1221no—
179C2×C42—611no—
180C2×C16—1222no—
181C2×C16—1222no—
182C2×C16—2442no—
183C4⋊C8—611no—
184C4⋊C8—1221no—
185C4⋊C8—1221no—
186C4⋊C8C2×#692311yescharacteristic
187C22⋊C8—21no—
188C22⋊C8—1221no—
189C22⋊C8—1221no—
190#97—1221no—
191#97—1221no—
192C4×C8—611no—
193C4×C8—611no—
194C4×C8—611no—
195C4×C8—1221no—
196C4×C8C2×#692311yescharacteristic
197C2×Q8—611no—
198C2×D4—1221no—
199C2×D4D61⋊C811yescharacteristic
200C22×C4—21no—
201C22×C4—611no—
202C22×C4—611no—
203C22×C4—611no—
204M16—42no—
205C2×C8—21no—
206C2×C8—611no—
207C2×C8—611no—
208C2×C8—1221no—
209C2×C8—1221no—
210C2×C8—1221no—
211C2×C8—2441no—
212C2×C8—2441no—
213C2×C8—2441no—
214C2×C8C22⋊#692311yescharacteristic
215C2×C8C22⋊#692311yescharacteristic
216C4⋊C4—611no—
217C4⋊C4—1221no—
218C4⋊C4—1221no—
219C4⋊C4—1221no—
220C4⋊C4—1221no—
221C4⋊C4D61⋊C811yescharacteristic
222C22⋊C4—21no—
223C22⋊C4—1221no—
224C22⋊C4—1221no—
225C22⋊C4—1221no—
226C22⋊C4—1221no—
227C42—611no—
228C42—611no—
229C42—611no—
230C42—1221no—
231C42C22×#692311yescharacteristic
232C16—2442no—
233C16—2442no—
234C23—21no—
235C23—611no—
236Q8—1222no—
237D4—22no—
238D4—2442no—
239C2×C4—21no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—611no—
243C2×C4—611no—
244C2×C4—611no—
245C2×C4—1222no—
246C2×C4—1221no—
247C2×C4—1221no—
248C2×C4—1222no—
249C2×C4—1221no—
250C2×C4—1221no—
251C2×C4C2×C22⋊#692311yescharacteristic
252C2×C4C2×D61⋊C811yescharacteristic
253C2×C4D61⋊M1611yescharacteristic
254C8—21no—
255C8—21no—
256C8—41no—
257C8—611no—
258C8—611no—
259C8—1221no—
260C8—2441no—
261C22—41no—
262C22—41no—
263C22—41no—
264C22—612no—
265C22—1221no—
266C22—1221no—
267C22D61⋊(C22⋊C8)11yescharacteristic
268C4—21no—
269C4—41no—
270C4—1221no—
271C4—1221no—
272C4—1221no—
273C4—2441no—
274C4—2441no—
275C4#1684075311yescharacteristic
276C4#1684076011yescharacteristic
277C4#1684082112yes—
278C2—81no—
279C2—1222no—
280C2#2146111511yescharacteristic
281C2#2146205011yescharacteristic
282C2D61⋊#35011yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC42C22×#6923
FittingC61×#436C4
socleC22×C61C2×C22⋊C8
prime radical#14519748C8
cosocleC4×#92418C23
hypercenter#436#6923
hypocenterC61#11622
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #436

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #21462178C2semidirect
2. D61⋊(C4⋊C16)C2semidirect
3. #21460786C2semidirect
4. D4⋊#11758187C2semidirect
164. C61#11622semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214621782
D61⋊(C4⋊C16)2
#214607862
D4⋊#117581872
#214547972
#1162261